In the present work, characteristics of large‐amplitude (>150 m) Kelvin–Helmholtz (KH) billows in the lower atmosphere are analysed, with emphasis on the turbulent properties. First, past studies are reviewed. Almost all the studies reported gradient Richardson number (Ri) close to 0.25. Results of observations in the height range 1.32–20.34 km using 46.5 MHz middle and upper atmosphere radar (MUR; Japan, 34.85°N, 136.10°E) are then described. A total of ∼600 h of data at high vertical and range resolutions was used. Except for very few cases, trains of KH braids are not followed by layer splitting, which can eventually result from turbulent mixing. A particular event shows some sort of turbulent plumes at the interface between a nearly neutral layer and a stable layer in the tropopause region. These turbulent plumes likely arose as the result of entrainment at the stable layer interface produced by still active turbulent mixing. Statistics on the characteristics of the KH billows are also presented. Large‐amplitude KH billows in the lower atmosphere were only present less than 0.6% of the time and height. The typical depth, horizontal wavelength and depth‐to‐wavelength ratio of the KH braids are about 600 m, 2600 m and 0.22, respectively. They are thus relatively shallow and the quasi‐absence of layer splitting may suggest that they are more frequently generated when Ri falls just below 0.25 (so that the large‐amplitude KH billows are not sufficiently energetic for breaking and mixing). Vertical shears of horizontal wind are about 23 ms⁻¹ km⁻¹ on average. Finally, attempts at estimating (maximum) energy dissipation rate ε and (minimum) vertical eddy diffusivity K are made. Mean values of ε_max and K_min are typically ∼1 mW kg⁻¹ (77% in the range 0.15–3.0 mW kg⁻¹) and ∼5 m² s⁻¹ (70% in the range 1–10 m² s⁻¹), respectively. Copyright © 2011 Royal Meteorological Society

Turbulence parameters in the lower troposphere (up to ~4.5 km) are estimated from measurements of high-resolution and fast-response cold-wire temperature and Pitot tube velocity from sensors onboard DataHawk Unmanned Aerial Vehicles (UAVs) operated at the Shigaraki Middle and Upper atmosphere (MU) Observatory during two ShUREX (Shigaraki UAV Radar Experiment) campaigns in 2016 and 2017. The practical processing methods used for estimating turbulence kinetic energy dissipation rate $\epsilon$ and temperature structure function parameter $C_T^2$ from one-dimensional wind and temperature frequency spectra are first described in detail. Both are based on the identification of inertial (−5/3) subranges in respective spectra. Using a formulation relating $\epsilon$ and $C_T^2$ valid for Kolmogorov turbulence in steady state, the flux Richardson number $R_f$ and the mixing efficiency ${\chi }_m$ are then estimated. The statistical analysis confirms the variability of $R_f$ and ${\chi }_m$ around $~0.13-0.14$ and $~0.16-0.17$ , respectively, values close to the canonical values found from some earlier experimental and theoretical studies of both the atmosphere and the oceans. The relevance of the interpretation of the inertial subranges in terms of Kolmogorov turbulence is confirmed by assessing the consistency of additional parameters, the Ozmidov length scale $L_O$ , the buoyancy Reynolds number $R{e}_b$ , and the gradient Richardson number Ri. Finally, a case study is presented showing altitude differences between the peaks of $N^2$ , $C_T^2$ and $\epsilon$ , suggesting turbulent stirring at the margin of a stable temperature gradient sheet. The possible contribution of this sheet and layer structure on clear air radar backscattering mechanisms is examined.

The WPR-LQ-7 is a UHF (1.3575 GHz) wind profiler radar used for routine measurements of the lower troposphere at Shigaraki MU Observatory (34.85^∘ N, 136.10^∘ E; Japan) at a vertical resolution of 100 m and a time resolution of 10 min. Following studies carried out with the 46.5 MHz middle and upper atmosphere (MU) radar (Luce et al., 2018), we tested models used to estimate the rate of turbulence kinetic energy (TKE) dissipation ε from the Doppler spectral width in the altitude range ∼ 0.7 to 4.0 km above sea level (a.s.l.). For this purpose, we compared LQ-7-derived ε using processed data available online (http://www.rish.kyoto-u.ac.jp/radar-group/blr/shigaraki/data/, last access: 24 July 2023) with direct estimates of ε (ε_U) from DataHawk UAVs. The statistical results reveal the same trends as reported by Luce et al. (2018) with the MU radar, namely (1) the simple formulation based on dimensional analysis ${\mathit{\epsilon }}_{L_{\mathrm{out}}}={\mathit{\sigma }}^{\mathrm{3}}/L_{\mathrm{out}}$ , with L_out∼70 m, provides the best statistical agreement with ε_U. (2) The model ε_N predicting a σ²N law (N is Brunt–Vaïsälä frequency) for stably stratified conditions tends to overestimate for ${\mathit{\epsilon }}_{\mathrm{U}}\lesssim \mathrm{5}\times {\mathrm{10}}^{-\mathrm{4}}$ m² s⁻³ and to underestimate for ${\mathit{\epsilon }}_{\mathrm{U}}\gtrsim \mathrm{5}\times {\mathrm{10}}^{-\mathrm{4}}$ m² s⁻³. We also tested a model ε_S predicting a σ²S law (S is the vertical shear of horizontal wind) supposed to be valid for low Richardson numbers ($\mathit{Ri}=N^{\mathrm{2}}/S^{\mathrm{2}}$ ). From the case study of a turbulent layer produced by a Kelvin–Helmholtz (K–H) instability, we found that ε_S and ${\mathit{\epsilon }}_{L_{\mathrm{out}}}$ are both very consistent with ε_U, while ε_N underestimates ε_U in the core of the turbulent layer where N is minimum. We also applied the Thorpe method from data collected from a nearly simultaneous radiosonde and tested an alternative interpretation of the Thorpe length in terms of the Corrsin length scale defined for weakly stratified turbulence. A statistical analysis showed that ε_S also provides better statistical agreement with ε_U and is much less biased than ε_N. Combining estimates of N and shear from DataHawk and radar data, respectively, a rough estimate of the Richardson number at a vertical resolution of 100 m (Ri₁₀₀) was obtained. We performed a statistical analysis on the Ri dependence of the models. The main outcome is that ε_S compares well with ε_U for low Ri₁₀₀ (Ri₁₀₀≲1), while ε_N fails. ${\mathit{\epsilon }}_{L_{\mathrm{out}}}$ varies as ε_S with Ri₁₀₀, so that ${\mathit{\epsilon }}_{L_{\mathrm{out}}}$ remains the best (and simplest) model in the absence of information on Ri. Also, σ appears to vary as ${\mathit{Ri}}_{\mathrm{100}}^{-\mathrm{1}/\mathrm{2}}$ when Ri₁₀₀≳0.4 and shows a degree of dependence on S₁₀₀ (vertical shear at a vertical resolution of 100 m) otherwise.

This paper deals with the detection and quantification of refractivity turbulence in the troposphere from radiosonde and very high frequency (VHF) band radar data. Balloon data processing methods based on Thorpe sorting and recently developed by Wilson et al. (2010, 2011, and 2013) can be applied for a direct identification of turbulent layers from the in situ profiles. The VHF band mid and upper atmosphere radar (MUR) can be operated in range‐imaging mode for detecting and monitoring turbulent layers at high time and range resolutions (of the order of 10 s and a few tens of meters, respectively). For cross validating the techniques, concurrent MUR and RS92‐SGP Vaisala radiosonde observations were made at the Shigaraki Middle and Upper atmosphere (MU) observatory (34.85°N, 136.15°E; Japan) during a field campaign of 3 weeks in September 2011. The radar signature, in terms of echo power and aspect ratio, of the turbulent layers identified from balloon data analyses is investigated from case studies and statistics. The deep (> ~100 m) layers are very often associated with echo power maxima and weak aspect ratios suggesting that the same events of isotropic turbulence were detected by both instruments. Some others are associated with relative minima of isotropic echo power, possibly indicating a later stage of turbulence. The ranges of strong aspect ratios are generally not associated with turbulent events in the balloon data supporting the hypothesis that anisotropic turbulence is not the cause of vertically enhanced radar echoes. Quantitative comparisons are made between radar echo power and refractive index constant structure estimated from temperature variance and additional parameters in the selected layers. Despite a large scatter between the radar and balloon estimates, the results are statistically significant (correlation coefficients ~0.5–0.88) even when the causes of systematic decrease with height of(humidity and density) are removed. Our studies therefore demonstrate that radar and balloon observations of turbulence are consistent between each other and that new insights on tropospheric turbulence can be obtained by the two techniques as stand‐alone systems.

The potential ability of VHF or UHF Doppler radars to measure turbulence kinetic energy (TKE) dissipation rate ε in the atmosphere is a major asset of these instruments because of the possibility to continuously monitor turbulence in the atmospheric column above the radars. Several models have been proposed over the past decades to relate ε to half the Doppler spectral width σ, corrected for non-turbulent contributions, but their relevance remains unclear. Recently, Luce et al. (2023) tested the performance of a new model expected to be valid for weakly stratified or strongly sheared conditions, i.e., for low Richardson (Ri) numbers. Its simplest expression is ε_S=C_Sσ²S, where C_S∼0.64 and $S=|\mathrm{d}\mathit{V}/\mathrm{d}z|$ is the vertical shear of the horizontal wind V. We assessed the relevance of this model with a UHF (1.357 GHz) wind profiler called WPR LQ-7, which is routinely operated at the Shigaraki Middle and Upper Atmosphere (MU) observatory (34.85^∘ N, 136.10^∘ E) in Japan. For this purpose, we selected turbulence events associated with Kelvin–Helmholtz (KH) billows, because their formation necessarily requires Ri<0.25 somewhere in the flow, a condition a priori favorable to the application of the model. Eleven years of WPR LQ-7 data were used for this objective. The assessment of ε_S was first based on its consistency with an empirical model ${\mathit{\epsilon }}_{\text{Lout}}={\mathit{\sigma }}^{\mathrm{3}}/L_{\text{out}}$ , where L_out has the dimension of an outer scale of turbulence. It was found to compare well in a KH layer with direct estimates of ε from in situ measurements for L_out≈70 m. Some degree of equivalence between ε_S and ε_Lout was confirmed by statistical analysis of 192 KH layers found in the height range 0.3–5.0 km indicating that $L_{\text{out}}\approx L_{\mathrm{H}}/\mathrm{0.64}$ , where $L_{\mathrm{H}}=\mathit{\sigma }/S$ is the Hunt scale defined for neutral turbulence. The degree of equivalence is even significantly improved if L_out is not treated as a constant but depends on the depth D of the layer. We found L_out≈0.0875D or equivalently L_H∼0.056D, which also means that σ is proportional to the apparent variation in the horizontal velocity (S×D) over the depth of the KH layer. Consequently, ε_S=0.64σ²S and ${\mathit{\epsilon }}_{\text{Lout}}={\mathit{\sigma }}^{\mathrm{3}}/\mathrm{0.0875}D$ would express the same model for KH layers when Ri remains low. For such a condition, we provide a physical interpretation of ε_Lout, which would be qualitatively identical to that for neutral boundary layers.

Under stably stratified conditions, the dissipation rate ε of turbulence kinetic energy (TKE) is related to the structure function parameter for temperature , through the buoyancy frequency and the so-called mixing efficiency. A similar relationship does not exist for convective turbulence. In this paper, we propose an analytical expression relating ε and in the convective boundary layer (CBL), by taking into account the effects of nonlocal heat transport under convective conditions using the Deardorff countergradient model. Measurements using unmanned aerial vehicles (UAVs) equipped with high-frequency response sensors to measure velocity and temperature fluctuations obtained during the two field campaigns conducted at Shigaraki MU observatory in June 2016 and 2017 are used to test this relationship between ε and in the CBL. The selection of CBL cases for analysis was aided by auxiliary measurements from additional sensors (mainly radars), and these are described. Comparison with earlier results in the literature suggests that the proposed relationship works, if the countergradient term γ _D in the Deardorff model, which is proportional to the ratio of the variances of potential temperature θ and vertical velocity w, is evaluated from in situ (airplane and UAV) observational data, but fails if evaluated from large-eddy simulation (LES) results. This appears to be caused by the tendency of the variance of θ in the upper part of the CBL and at the bottom of the entrainment zone to be underestimated by LES relative to in situ measurements from UAVs and aircraft. We discuss this anomaly and explore reasons for it.